The median procedure on median graphs Original Research Article

A median of a profile π = (x1, …, xk) of vertices of a finite connected graph G is a vertex x for which ∑ki = 1 d(x, xi) is minimum, where d is the usual geodesic distance on G. The function Med whose domain is the set of all profiles and is given by Med(π) = {x: x is a median of π} is called the median procedure on G. In this paper, the median procedure is characterized for median graphs and cube-free median graphs.